A permutation σ ∈ Sn is a k-separator if all of its patterns of length k are distinct. Let F (k) denote the maximal length of a k-separator. Hegarty (2013) showed that k + ⌊√ 2k − 1 ⌋ − 1 6 F (k) 6 k + ⌊√ 2k − 3 ⌋ , and conjectured that F (k) = k + ⌊√ 2k − 1 ⌋ − 1. This paper will strengthen the upper bound to prove the conjecture for all sufficiently large k (in particular, for all k > 320801).

Separators in graphs are instrumental in the design of algorithms, having proven to be the key technical tool in approximation algorithms for many optimization problems. In the geometric setting, this naturally translates into the study of separators in the intersection graphs of geometric objects. Recently a number of new separator theorems have been proven for the case of geometric objects in...

A graph is called threshold if there exists a real number b and real numbers aj associated with its vertices w, such that ims a, < b holds iff S is a stable (independent) set of vertices. The vector (a ,..., a; b) associated to a threshold graph is called an integral separator if ai + a > b + 1 for every edge (w,, wj). A simple algorithm is presented to determine for a given threshold graph its...

The ion-optical characteristics of the separator should meet the requirements of the antiproton beam, the parameters of which are given in Table 1. The magnetic bending power is 13 Tm; the transverse acceptance is 240 mm mrad; the momentum acceptance is 6 %. These parameters require magnets with large aperture, especially in the horizontal plane (up to 400 mm). The ion optics of the antiproton ...

The TRIμP facility, under construction at KVI, requires the production and separation of short-lived and rare isotopes. Direct reactions, fragmentation and fusionevaporation reactions in normal and inverse kinematics are foreseen to produce nuclides of interest with a variety of heavy-ion beams from the superconducting cyclotron AGOR. For this purpose, we have designed, constructed and commissi...

The file transfer committee met and discussed the Mail Box Protocol RFC 221, NIC 7612. The potential utility for the mechanism was confirmed and a couple of changes suggested. We first give the changes and then restate the Protocol. CHANGES 1) The Mail Box Protocol is only to allow ASCII stings of text formatted for a network standard line printer rather than allowing other data types. 2) A new...

For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum vertex separator. For a connected graph G with vertex connectivity k (k ≥ 1), the connectivity augmentation refers to a set S of edges whose augmentation toG...

INTRODUCTION Serum blood collection tubes with separator gel are widely used by many laboratories for chemistry analyses. We describe a case of a primary blood collection tube filled with blood sample and a floating separator gel. MATERIALS AND METHODS The blood sample was collected from a 51 years old female in intensive care unit with the diagnosis of pneumonia into a BD Vacutainer SST tube...

the sharp upper bounds and the sharp lower bounds of the largest eigenvalues $lambda_1$, the least eigenvalue $lambda_n$, the second largest eigenvalue $lambda_2$, the spread and the separator among all firefly graphs on $n$ vertices are determined.

A thermodynamic approach is presented to classify geothermal reservoir as vapor or liquid dominated. According to it, the vapor dominated reservoir has specific volume of fluid (i.e. combined vapor and liquid) greater than the critical volume of water whereas the liquid dominated reservoir has lesser specific volume. Enthalpy is not a conservative entity in a geothermal system. Apart from it, t...